母线作图

母线作图
几何画板及绘图内容加载中,请稍等……
2014-02-14 01:12
本范例展示了折纸活动中发现的母线现象。核心数学概念包括相似三角形和角平分线。通过使用Polygon, Point, Segment, AngularBisector等GeoGebra命令,可以构造出复杂的几何图形。适合用于几何作图的教学演示。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → veelhoek1, a, b, c, d, C, D
  2. Polygon(I, J, 4) → veelhoek3, i, j, k, l, K, L
  3. Point(d) → Q
  4. Point(b) → R
  5. Segment(Q, R) → r
  6. Point(k) → U
  7. Point(j) → V
  8. Segment(U, V) → t
  9. AngularBisector(d, r) → b_1, c_1
  10. AngularBisector(r, b) → d_1, e_1
  11. AngularBisector(r, a) → f_1, g_1
  12. AngularBisector(c, r) → h_1, i_1
  13. Intersect(e_1, c) → A_1
  14. Segment(A_1, R) → j_1
  15. Intersect(i_1, d) → B_1
  16. Intersect(i_1, b) → C_1
  17. Segment(B_1, C_1) → k_1
  18. Intersect(c_1, c) → D_1
  19. Segment(Q, D_1) → l_1
  20. Intersect(b_1, a) → E_1
  21. Segment(Q, E_1) → m_1
  22. Intersect(d_1, a) → F_1
  23. Segment(F_1, R) → n_1
  24. Intersect(f_1, d) → G_1
  25. Intersect(f_1, b) → H_1
  26. Segment(G_1, H_1) → p_1
  27. Intersect(j_1, l_1) → I_1
  28. Intersect(j_1, k_1) → J_1
  29. Intersect(k_1, l_1) → K_1
  30. Intersect(m_1, p_1) → L_1
  31. Intersect(n_1, p_1) → M_1
  32. Intersect(m_1, n_1) → N_1
  33. AngularBisector(t, k) → e, f
  34. AngularBisector(t, j) → g, h
  35. AngularBisector(t, l) → s, q_1
  36. AngularBisector(t, i) → r_1, s_1
  37. Intersect(s, k) → G
  38. Intersect(s, i) → H
  39. Segment(G, H) → t_1
  40. Intersect(g, i) → S
  41. Segment(S, V) → a_2
  42. Intersect(e, l) → T
  43. Segment(T, U) → b_2
  44. Intersect(f, j) → O_1
  45. Segment(U, O_1) → c_2
  46. Intersect(h, k) → P_1
  47. Segment(P_1, V) → d_2
  48. Intersect(r_1, l) → Q_1
  49. Intersect(r_1, j) → R_1
  50. Segment(Q_1, R_1) → e_2
  51. Intersect(g, l) → S_1
  52. Segment(S_1, V) → f_2
  53. Intersect(e, i) → T_1
  54. Segment(U, T_1) → g_2
  55. Intersect(t_1, g_2) → U_1
  56. Intersect(e_2, g_2) → V_1
  57. Intersect(f_2, g_2) → W_1
  58. Intersect(t_1, f_2) → Z_1
  59. Intersect(e_2, f_2) → A_2
  60. Intersect(c_2, d_2) → B_2
  61. Intersect(b_2, e_2) → C_2
  62. Intersect(t_1, b_2) → D_2
  63. Intersect(t_1, e_2) → E_2
  64. Intersect(t_1, a_2) → F_2
  65. Intersect(a_2, e_2) → G_2
  66. Point(c) → H_2
  67. Point(a) → I_2
  68. Segment(H_2, I_2) → h_2
  69. Point(d) → J_2
  70. Point(b) → K_2
  71. Segment(J_2, K_2) → i_2
  72. Intersect(b, c) → L_2
  73. Intersect(a, d) → M_2
  74. Segment(L_2, M_2) → j_2
  75. Point(k) → N_2
  76. Point(l) → P_2
  77. Point(j) → Q_2
  78. Segment(P_2, Q_2) → l_2
  79. Intersect(k, l) → R_2
  80. Intersect(i, j) → S_2
  81. Segment(R_2, S_2) → m_2
  82. Intersect(j, k) → T_2
  83. Intersect(i, l) → U_2
  84. Segment(T_2, U_2) → n_2
  85. Intersect(c, d) → V_2
  86. Intersect(a, b) → W_2
  87. Segment(V_2, W_2) → p_2
  88. Intersect(i, l) → Z_2
  89. Intersect(k, l) → A_3
  90. Ray(Z_2, A_3) → q_2
  91. Line(U, V) → r_2
  92. Intersect(i, j) → B_3
  93. Ray(Z_2, B_3) → s_2
  94. Intersect(r_2, q_2) → C_3
  95. Intersect(r_2, s_2) → O
  96. Segment(C_3, A_3) → m
  97. Segment(C_3, U) → n
  98. Segment(V, O) → p
  99. Segment(O, B_3) → q
  100. Segment(A_2, O) → a_1
  101. Segment(U_1, C_3) → t_2
  102. Intersect(j, e_2) → P
  103. Segment(P, O) → a_3
  104. Intersect(k, t_1) → W
  105. Segment(C_3, W) → b_3
  106. OrthogonalLine(E_2, t) → c_3
  107. Intersect(c_3, t) → Z
  108. Circle(E_2, Z) → d_3
  109. OrthogonalLine(B_2, t) → e_3
  110. Intersect(e_3, t) → D_3
  111. Circle(B_2, D_3) → f_3
  112. OrthogonalLine(U_1, t) → g_3
  113. Intersect(g_3, t) → E_3
  114. OrthogonalLine(U_1, l) → i_3
  115. Intersect(i_3, l) → F_3
  116. OrthogonalLine(D_2, k) → j_3
  117. Intersect(j_3, k) → G_3
  118. Ray(Q, R) → l_3
  119. Intersect(c, d) → H_3
  120. Intersect(b, c) → I_3
  121. Ray(H_3, I_3) → m_3
  122. Intersect(l_3, m_3) → J_3
  123. Segment(I_3, J_3) → n_3
  124. Segment(J_3, R) → p_3
  125. Intersect(b, k_1) → K_3
  126. Segment(K_3, J_3) → q_3
  127. OrthogonalLine(K_1, c) → r_3
  128. Intersect(r_3, c) → L_3
  129. Circle(K_1, L_3) → s_3
  130. Intersect(a, b) → M_3
  131. Intersect(a, d) → N_3
  132. Line(M_3, N_3) → t_3
  133. Line(R, Q) → a_4
  134. Intersect(t_3, a_4) → O_3
  135. Segment(O_3, Q) → b_4
  136. Segment(O_3, N_3) → c_4
  137. Intersect(d, p_1) → P_3
  138. Segment(O_3, P_3) → d_4
  139. OrthogonalLine(M_1, b) → e_4
  140. Intersect(e_4, b) → Q_3
  141. Circle(M_1, Q_3) → f_4
  142. OrthogonalLine(J_1, c) → g_4
  143. OrthogonalLine(L_1, a) → h_4
  144. Intersect(g_4, c) → R_3
  145. Intersect(h_4, a) → S_3
  146. Circle(J_1, R_3) → k_4
  147. Circle(L_1, S_3) → p_4
  148. OrthogonalLine(G_2, i) → i_4
  149. Intersect(i_4, i) → T_3
  150. Midpoint(k) → U_3
  151. Midpoint(i) → V_3
  152. Segment(U_3, V_3) → k_2
  153. OrthogonalLine(D_2, k) → h_3
  154. OrthogonalLine(G_2, i) → k_3
  155. Intersect(h_3, k) → W_3
  156. Intersect(k_3, i) → Z_3
  157. Circle(D_2, W_3) → q_4
  158. Circle(G_2, Z_3) → r_4
  159. OrthogonalLine(U_1, k) → j_4
  160. OrthogonalLine(A_2, i) → l_4
  161. Intersect(j_4, k) → A_4
  162. Intersect(l_4, i) → B_4
  163. Circle(U_1, A_4) → s_4
  164. Circle(A_2, B_4) → t_4

AI 绘图提示语参考

绘制一个由多个三角形和线段组成的复杂几何图形。首先绘制两个四边形,然后在四边形的边和对角线上找到中点,连接这些中点形成新的线段。接着,利用角平分线构造方法,从这些线段出发,逐步构造出更多的线段和交点,最终形成一个由多个三角形和线段交织而成的复杂图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。